Final answer:
To solve |f + 9| = 81, we consider that f + 9 can be either 81 or -81. Solving both equations, we find that the solutions are f = 72 and f = -90.
Step-by-step explanation:
To solve the equation |f 9| = 81 for f, we can interpret the absolute value expression as representing two possible cases because the absolute value of a number is the distance from zero on the number line, which is always positive or zero. For the expression inside the absolute value to be equal to 81, it can either be 81 itself or -81. Therefore, we set up two equations: f + 9 = 81 and f + 9 = -81.
- For the first equation, we subtract 9 from both sides to isolate f, which gives us f = 72.
- For the second equation, we again subtract 9 from both sides to isolate f, resulting in f = -90.
Thus, the solutions to the equation are f = 72 and f = -90.